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Pearson Algebra 1 Common Core, 2011

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Pearson Algebra 1 Common Core, 2011 View details

1. Solving One-Step Equations

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Exercise 59 Page 86

Isolate r on one side of the equation.

31 14

Practice makes perfect

To solve the equation, we have to isolate r on one side. We will start by rewriting the mixed number as an improper fraction. Then, we will use the Multiplication Property of Equality and multiply both sides of the equation by 5. This will eliminate the denominator of the fraction and isolate r.

6 14=r/5

▼

Write mixed number as a fraction

a bc=a* c+b/c

6*4+1/4=r/5

Multiply

24+1/4=r/5

Add terms

25/4=r/5

LHS * 5=RHS* 5

25/4 * 5=r/5 * 5

FracMultDenomToNumber

a/5* 5 = a

25/4*5=r

MoveRightFacToNum

a/c* b = a* b/c

25*5/4=r

Multiply

125/4=r

Rearrange equation

r=125/4

Therefore, r= 1254 is the solution to the equation. To check that we have the correct solution, we can substitute r= 1254 into the original equation and simplify.

6 14? =r/5

▼

Write mixed number as a fraction

a bc=a* c+b/c

6*4+1/4? =r/5

Multiply

24+1/4? =r/5

Add terms

25/4? =r/5

r= 125/4

25/4? =. 125/4 /5.

.a/b /c.= a/b* c

25/4? =125/4*5

Multiply

25/4? =125/20

a/b=.a /5./.b /5.

25/4? =125/5/20/5

Calculate quotient

25/4=25/4 ✓

Since the left-hand side and the right-hand side are equal, r= 1254 is the correct solution. However, we can also write our answer as a mixed number.

r=125/4

▼

Write as mixed number

Rewrite 125 as 124+1

r=124+1/4

Write as a sum of fractions

r=124/4+1/4

Calculate quotient

r=31+1/4

Finally, the numeric expression 31+ 14 can be read as 31 and 14. Therefore, it can be written as 31 14. y=31+1/4 ⇔ y=31 14

Subchapter links

Lesson Check p.85

Practice and Problem-Solving Exercises p.85-87

Standardized Test Prep p.87

Mixed Review p.87